List of Publications
Monographs:
- A. Lomtatidze, S. Mughigulashvili,
Some two-poit boundary value problems for second order functional differential
equations,
Folia Facul. Sci. Natur. Univ. Masar. Brun., Mathematica 8,
Brno: Masaryk University, 2000, 72 pages.
- R. Hakl, A. Lomtatidze, J. Šremr,
Some boundary value problems for first order scalar functional differential
equations,
Folia Facul. Sci. Natur. Univ. Masar. Brun., Mathematica 10,
Brno: Masaryk University, 2002, 300 pages.
Reprint
- R. Hakl, A. Lomtatidze, I. P. Stavroulakis,
Bounded solutions to the first-order scalar finctional differential equations,
Mem. Differential Equations Math. Phys. 59 (2013), 1-104.
Reprint
Articles:
- A. Lomtatidze,
On a boundary value problem for second order linear differential equations with
nonintegrable singularities,
Proc. I. Vekua Inst. Appl. Math. 14 (1983), 136-144, in Russian.
- A. Lomtatidze, I. Kiguradze,
On certain boundary value problems for second order ordinary differential
equations with singularities,
J. Math. Anal. Appl. 101 (1984), No. 2, 325-347.
Reprint
- A. Lomtatidze,
On a singular boundary value problem for second order linear differential
equations,
Boundary Value Problems, Perm (1984), 46-50.
- A. Lomtatidze,
On solvability of boundary value problems for second order nonlinear differential
equations with singularities,
Rep. of enlarged session of the seminar of I. Vekua Inst. Appl. Math. 1985,
Vol. 1 (1985), No. 3, 85-92, in Russian.
- A. Lomtatidze,
On oscillatory properties of solutions of second order linear differential
equations,
Seminar of I. Vekua Inst. Appl. Math. Reports. 19 (1985), 39-53, in Russian.
- A. Lomtatidze,
On a singular three-point boundary value problem,
Proc. I. Vekua Inst. Appl. Math. 17 (1986), 122-133, in Russian.
- A. Lomtatidze,
On a boubdary value problem for second order nonlinear ordinary differential equations
with singularities,
Differ. Uravn. 22 (1986), No. 3, 416-426, in Russian.
- A. Lomtatidze,
On positive solutions of singular boundary value problems for second order
nonlinear ordinary differential equations,
Differ. Uravn. 22 (1986), No. 6, 1092, in Russian.
- A. Lomtatidze, N. Kandelaki,
On the approximate solution of a certain evolution equation,
Comp. Math. and Programming 27 (1987), No. 1, 85-90, in Russian.
- A. Lomtatidze,
On positive solutions of boundary value problems for second order ordinary differential
equations with singularities,
Differ. Uravn. 23 (1987), No. 10, 1685-1692, in Russian.
- A. Lomtatidze,
Concerning solvability of singular boundary value problems for second order ordinary
differential equations,
Proc. I. Vekua Inst. Appl. Math. 22 (1987), 135-149, in Russian.
- A. Lomtatidze,
On some boundary value problems for two-dimensional differential systems,
Rep. of enlarged session of the seminar of I.Vekua Inst. Appl. Math. 1992,
Vol. 7 (1992), No. 3, 68-70.
- A. Lomtatidze,
On some two-poit boundary value problems for two-dimensional systems of ordinary
differential equations,
Georgian Math. J. 1 (1994), No. 3, 303-314.
Reprint
- A. Lomtatidze,
Existence of conjugate points for second order linear differential equations,
Georgian Math. J. 2 (1995), No. 1, 93-98.
Reprint
- A. Lomtatidze,
Nonlocal boundary value problem for second order linear ordinary differential
equations,
Differ. Uravn. 31 (1995), No. 3, 446-455, in Russian.
- A. Lomtatidze,
On a nonlocal boundary value problem for second order linear ordinary differential
equations,
J. Math. Anal. Appl. 193 (1995), No. 2, 889-908.
Reprint
- A. Lomtatidze, N. Partsvania,
On oscillatory properties of second order systems of ordinary differential
equations,
Mem. Differential Equations Math. Phys. 5 (1995), 122-124.
Reprint
- A. Lomtatidze, S. Mughigulashvili,
On periodic solutions of second order functional differential equations,
Mem. Differential Equations Math. Phys. 5 (1995), 125-126.
Reprint
- A. Lomtatidze,
On oscillation of third order linear differential equation,
Differ. Uravn. 32 (1996), No. 10, 1348-1354, in Russian.
- A. Lomtatidze,
Oscillation and nonoscillation of Emden-Fowler type equation of second
order,
Arch. Math. (Brno) 32 (1996), No. 3, 181-193.
Reprint
- A. Lomtatidze,
Oscillation and nonoscillation criteria for second order linear differential
equation,
Georgian Math. J. 4 (1997), No. 2, 129-138.
Reprint
- A. Lomtatidze, N. Partsvania,
Oscillation and nonoscillation criteria for two-dimensional system of first order
linear ordinary differential equations,
Georgian Math. J. 6 (1999), No. 3, 285-298.
Reprint
- A. Lomtatidze, T. Chantladze, N. Kandelaki,
Oscillation and nonoscillation criteria for a second order linear
equations,
Georgian Math. J. 6 (1999), No. 5, 401-414.
Reprint
- A. Lomtatidze, T. Chantladze, N. Kandelaki,
On zeros of solutions of a second order singular half-linear equation,
Mem. Differential Equations Math. Phys. 7 (1999), 127-158.
Reprint
- O. Došlý, A. Lomtatidze,
Disconjugacy and disfocality criteria for second order singular half-linear
differential equations,
Ann. Polon. Math. 72 (1999), No. 3, 273-284.
Reprint
- A. Lomtatidze, N. Kandelaki, D. Ugulava,
On oscillation and nonoscillation of second order half-linear equations,
Georgian Math. J. 7 (2000), No. 2, 329-346.
Reprint
- A. Lomtatidze, L. Malaguti,
On a nonlocal boundary value problem for second order singular
equations,
Georgian Math. J. 7 (2000), No. 2, 133-157.
Reprint
- A. Lomtatidze, N. Kandelaki, T. Chantladze,
The p-Laplacian and connected pairs of functions,
Mem. Differential Equations Math. Phys. 20 (2000), 113-126.
Reprint
- A. Lomtatidze, E. Bravyi, B. Půža,
A note on the theorem on differential inequalities,
Georgian Math. J. 7 (2000), No. 4, 627-631.
Reprint
- A. Lomtatidze, T. Chantladze, D. Ugulava,
Conjugacy and disconjugacy criteria fir second order linear ordinary deifferential
equations,
Arch. Math. (Brno) 36 (2000), No. 4, 313-323.
Reprint
- A. Lomtatidze, T. Chantladze, N. Kandelaki,
On quadratically integrable solutions of the second order linear
equation,
Arch. Math. (Brno) 37 (2001), No. 1, 57-62.
Reprint
- R. Hakl, A. Lomtatidze, B. Půža,
On nonnegative solutions of first order scalar functional differential
equations,
Mem. Differential Equations Math. Phys. 23 (2001), 51-84.
Reprint
- R. Hakl, A. Lomtatidze, B. Půža,
On periodic solutions of first order nonlinear functional differential equations
of non-Volterra's type,
Mem. Differential Equations Math. Phys. 24 (2001), 83-105.
Reprint
- A. Lomtatidze, L. Adamec,
Oscillation criteria for third order linear equations,
Differ. Uravn. 37 (2001), No. 6, 723-729, in Russian.
Reprint
- R. Hakl, A. Lomtatidze, B. Půža,
On periodic solutions of first order linear functional differential
equations,
Nonlin. Anal. 49 (2002), 929-945.
Reprint
- R. Hakl, A. Lomtatidze,
A note on the Cauchy problem for first order linear differential equations with
a deviating argument,
Arch. Math. (Brno) 38 (2002), No. 1, 61-71.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
On an antiperiodic type boundary value problem for first order linear functional
differential equations,
Arch. Math. (Brno) 38 (2002), No. 2, 149-160.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
On a periodic type boundary value problem for first order nonlinear functional
differential equations,
Nonlin. Anal. 51 (2002), 425-447.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
On constant sign solutions of a periodic type boundary value problems for first
order scalar functional differential equations,
Mem. Differential Equat. Math. Phys 26 (2002), 65-90.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
Solvability and unique solvability of a periodic type boundary value problems for
first order scalar functional differential equations,
Georgian Math. J. 9 (2002), No. 3, 525-547.
Reprint
- A. Lomtatidze, T. Chantladze, N. Kandelaki, D. Ugulava,
On a generalization of the Dirichlet integral,
Georgian Math. J. 9 (2002), No. 3, 449-459.
- R. Hakl, E. Bravyi, A. Lomtatidze,
Optimal conditions on unique solvability of the Cauchy problem for the first order
linear functional differential equations,
Czechoslovak Math. J. 52 (2002), No. 3, 513-530.
Reprint
- R. Hakl, E. Bravyi, A. Lomtatidze,
On Cauchy problem for the first order nonlinear functional differential
equations,
Czechoslovak Math. J. 52 (2002), No. 4, 673-690.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
On a periodic type boundary value problem for first order linear functional
differential equations,
Neliniini Koliv. 5 (2002), No. 3, 416-432.
Reprint
- R. Hakl, A. Lomtatidze, B. Půža,
New optimal conditions for unique solvability of the Cauchy problem for first order
linear functional differential equations,
Math. Bohemica 127 (2002), No. 4, 509-524.
Reprint
- A. Lomtatidze, P. Torres,
On a two-point boundary value problem for second order singular
equations,
Czechoslovak Math. J. 53 (2003), No. 1, 19-43.
Reprint
- A. Lomtatidze, L. Malaguti,
On a two-point boundary value problem for second order ordinary differential
equations with singularities,
Nonlin. Anal. 52 (2003), No. 6, 1553-1567.
Reprint
- R. Hakl, A. Lomtatidze, B. Půža,
On a boundary value problem for first order scalar functional differential
equations,
Nonlin. Anal. 53 (2003), No. 3-4, 391-405.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
On an antiperiodic type boundary-value problem for first order
nonlinear functional differential equations of non-Volterra's
type,
Neliniini Koliv. 6 (2003), No. 4, 550-573.
Reprint
- R. Hakl, A. Lomtatidze, B. Půža,
On a periodic boundary value problem for the first order scalar
functional differential equation,
Differ. Uravn. 39 (2003), No. 3, 320-327, in Russian.
Reprint
- R. Hakl, A. Lomtatidze, I. P. Stavroulakis,
On a boundary value problem for scalar functional differential
equations,
Abstr. Appl. Anal. 2004 (2004), No. 1, 45-67.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
On nonnegative solutions of a periodic type boundary value problem for
first order scalar functional differential equations,
Funct. Differ. Equ. 11 (2004), No. 3-4, 363-394.
- A. Lomtatidze, Z. Opluštil,
On nonnegative solutions of a certain boundary value problem for
first order linear functional differential equations,
Electron. J. Qual. Theory Differ. Equ., Proc. 7th Coll. QTDE (2004), No. 16, 1-21.
Reprint
- R. Hakl, A. Lomtatidze, J. Šremr,
Solvability of a periodic type boundary value problem for first order
scalar functional differential equations,
Arch. Math. (Brno) 40 (2004), No. 1, 89-109.
Reprint
- A. Lomtatidze, P. Vodstrčil,
On nonnegative solutions of second order linear functional
differential equations,
Mem. Differential Equations Math. Phys. 32 (2004), 59-88.
Reprint
- A. Lomtatidze, P. Vodstrčil,
On sign constant solutions of certain boundary value problems for
second-order functional differential equations,
Appl. Anal. 84 (2005), No. 2, 197-209.
- A. Lomtatidze, H. Štěpánková,
On sign constant and monotone solutions of second order linear
functional differential equations,
Mem. Differential Equations Math. Phys. 35 (2005), 65-90.
Reprint
- O. Došlý, A. Lomtatidze,
Oscillation and nonoscillation criteria for half-linear second
order differential equations,
Hiroshima Math. J. 36 (2006), No. 2, 203-219.
Reprint
- A. Lomtatidze, P. Vodstrčil,
On Solvability of a three-point boundary value problem for
second order nonlinear functional differential equations,
Mem. Differential Equations Math. Phys. 40 (2007), 55-65.
Reprint
- A. Lomtatidze, Z. Opluštil, J. Šremr,
On a nonlocal boundary value problem for first order linear
functional differential equations,
Mem. Differential Equations Math. Phys. 41 (2007), 69-85.
Reprint
- A. Cabada, A. Lomtatidze, M. Tvrdý,
Periodic problem involving quasilinear differential operator and
weak singularity,
Adv. Nonlinear Stud. 7 (2007), No. 4, 629-649.
Reprint
- A. Lomtatidze, S. Mukhigulashvili, J. Šremr,
Nonnegative solutions of the characteristic initial value problem
for linear partial functional-differential equations of hyperbolic
type,
Math. Comput. Modelling 47 (2008), No. 11-12, 1292-1313.
Reprint
- I. Kiguradze, A. Lomtatidze,
On periodic solutions of linear differential equations with coefficients of
alternating sign,
Differ. Uravn. 44 (2008), No. 11, 1580-1581, in Russian.
- A. Lomtatidze, Z. Opluštil, J. Šremr,
Solvability conditions for a nonlocal boundary value problem for
linear functional differential equations,
Fasc. Math. 41 (2009), 81-96.
Reprint
- A. Lomtatidze, Z. Opluštil, J. Šremr,
Nonpositive solutions to a certain functional differential
inequality,
Nonlinear Oscil. 12 (2009), No. 4, 474-505.
Reprint
- I. Kiguradze, A. Lomtatidze,
Periodic solutions of nonautonomous ordinary differential
equations,
Monatsh. Math. 159 (2010), No. 3, 235-252.
Reprint
- A. Domoshnitsky, A. Lomtatidze, A. Maghakyan, J. Šremr,
Linear hyperbolic functional-differential equations with essentially bounded
right-hand side,
Abstr. Appl. Anal. 2011 (2011), ID 242965, 1-26.
Reprint
- A. Lomtatidze, J. Šremr,
On Oscillation of second-order linear ordinary differential equations,
Mem. Differential Equations Math. Phys. 54 (2011), 69-81.
Reprint
- A. Lomtatidze, J. Šremr,
On the Cauchy problem for linear hyperbolic functional-differential equations,
Czechoslovak Math. J. 62 (137) (2012), 391-440.
Reprint
- I. Kiguradze, A. Lomtatidze, N. Partsvania
Some multi-point boundary value problems for second order singular differential equations,
Mem. Differential Equations Math. Phys. 56 (2012), 133-141.
Reprint
- A. Lomtatidze, J. Šremr,
On oscillation and nonoscillation of two-dimensional linear differential systems,
Georgian Math. J. 20 (2013), No. 3, 573-600.
Reprint
- A. Lomtatidze, Z. Opluštil,
Fredholm alternative for the second-order singular Dirichlet problem,
Bound. Value Probl. 2014 (2014), No. 13, 1-15.
Reprint
- A. Lomtatidze, J. Šremr,
Carathéodory solutions to a hyperbolic differential inequality with a non-positive coefficient
and delayed arguments,
Bound. Value Probl. 2014 (2014), No. 52, 1-13.
Reprint
- A. Lomtatidze, Z. Opluštil,
Fredholm's third theorem for second-order singular Dirichlet problem,
Bound. Value Probl. 2014 (2014), No. 59, 1-12.
Reprint
- M. Dosoudilová, A. Lomtatidze, J. Šremr,
Oscillatory properties of solutions to certain two-dimensional systems of non-linear
ordinary differential equations,
Nonlin. Anal. 120 (2015), 57-75.
Reprint
Preprints:
- A. Lomtatidze, S. Mughigulashvili, J. Šremr
Nonnegative solutions of the characteristic initial value problem
for linear partial functional-differential equations of hyperbolic
type,
Mathematical Institute, Academy of Sciences of the Czech Republic,
Preprint 160 (2005).
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